Abstract

Subpicosecond Gaussian pulse propagation in an erbium-doped fiber amplifier is studied. An analytic expression for the pulse-broadening factor is obtained that includes the effects of gain, in addition to quadratic and cubic dispersion arising from the absorption and the emission spectra. The analytic results are compared with those obtained from numerical studies that incorporate precise gain and index wavelength dependences. Good agreement is obtained within the 1.53–1.56-µm wavelength range for input pulses as short as 0.25 ps.

© 1996 Optical Society of America

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References

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  1. F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
    [CrossRef]
  2. S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
    [CrossRef]
  3. D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
    [CrossRef]
  4. E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
    [CrossRef]
  5. J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
    [CrossRef]
  6. K. Tamura, E. Yoshida, T. Sugawa, and M. Nakazawa, “Broadband light generation by femtosecond pulse amplification with stimulated Raman scattering in a high-power erbium-doped fiber amplifier,” Opt. Lett. 20, 1631–1633 (1995).
    [CrossRef] [PubMed]
  7. D. J. Richardson, V. V. Alfanasjev, A. B. Grudinin, and D. N. Payne, “Amplification of femtosecond pulses in a passive, all-fiber soliton source,” Opt. Lett. 17, 1596–1598 (1992).
    [CrossRef] [PubMed]
  8. G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
    [CrossRef]
  9. W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
    [CrossRef]
  10. D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. 19, 1653–1660 (1980).
    [CrossRef] [PubMed]

1995 (3)

D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
[CrossRef]

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

K. Tamura, E. Yoshida, T. Sugawa, and M. Nakazawa, “Broadband light generation by femtosecond pulse amplification with stimulated Raman scattering in a high-power erbium-doped fiber amplifier,” Opt. Lett. 20, 1631–1633 (1995).
[CrossRef] [PubMed]

1994 (1)

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

1992 (1)

1991 (2)

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

1990 (2)

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

1980 (1)

Alfanasjev, V. V.

Barnes, W. L.

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

Desurvire, E.

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

Dianov, E. M.

D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
[CrossRef]

Endo, M.

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Fleming, S. C.

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

Ghosh, G.

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Grudinin, A. B.

Hall, K. L.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Haus, H. A.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Ippen, E. P.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Iwasaki, T.

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Korobkin, D. V.

D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
[CrossRef]

Laming, R. I.

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

LePage, S. M.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Marcuse, D.

Matera, F.

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

Moores, J. D.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Morkel, P. R.

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

Nakazawa, M.

Payne, D. N.

Rauschenbach, K. A.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Richardson, D. J.

Romagnoli, M.

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

Semenov, V. A.

D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
[CrossRef]

Settembre, M.

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

Sugawa, T.

Tamburrini, M.

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

Tamura, K.

Tarbox, E. J.

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

Whitley, T. J.

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

Wong, W. S.

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

Yoshida, E.

Appl. Opt. (1)

Electron. Lett. (2)

F. Matera, M. Romagnoli, M. Settembre, and M. Tamburrini, “Evaluation of chromatic dispersion in erbium-doped fibre amplifiers,” Electron. Lett. 27, 1867–1869 (1991).
[CrossRef]

S. C. Fleming and T. J. Whitley, “Measurement of pump induced refractive index change in erbium doped fibre amplifier,” Electron. Lett. 27, 1959–1961 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. L. Barnes, R. I. Laming, E. J. Tarbox, and P. R. Morkel, “Absorption and emission cross section of Er3+ doped silica fibers,” IEEE J. Quantum Electron. 27, 1004–1010 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. D. Moores, K. L. Hall, S. M. LePage, K. A. Rauschenbach, W. S. Wong, H. A. Haus, and E. P. Ippen, “20-GHz optical storage loop/laser using amplitude modulation, filtering, and artificial fast saturable absorption,” IEEE Photon. Technol. Lett. 7, 1096–1098 (1995).
[CrossRef]

J. Lightwave Technol. (3)

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

D. V. Korobkin, V. A. Semenov, and E. M. Dianov, “Anomolous dispersion in Er3+- and Yb3+-doped fibers,” J. Lightwave Technol. 13, 191–195 (1995).
[CrossRef]

E. Desurvire, “Study of the complex atomic susceptibility of erbium-doped fiber amplifiers,” J. Lightwave Technol. 8, 1517–1527 (1990).
[CrossRef]

Opt. Lett. (2)

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Figures (5)

Fig. 1
Fig. 1

Quadratic dispersion parameter, β2, showing contributions from erbium (β2E) and from the aluminosilicate host fiber (β2H).

Fig. 2
Fig. 2

Cubic dispersion parameter, β3, showing contributions from erbium (β3E) and from the aluminosilicate host fiber (β3H).

Fig. 3
Fig. 3

Gain dispersion parameters g1 and g2.

Fig. 4
Fig. 4

Linear pulse propagation for wavelengths (in micrometers) for (a) 1-ps, (b) 0.5-ps, and (c) 0.25-ps input pulses. Solid curves are the input pulses.

Fig. 5
Fig. 5

Pulse-broadening factors as determined from Eq. (12) (solid curves) and from the numerical studies (open triangles) as functions of wavelength for (a) 1-ps and (b) 0.5-ps input pulses. The dashed curves show the evaluation of the first two terms in Eq. (12) for g1=g2=β3=0. The dotted curves show the contribution from the host fiber alone.

Tables (1)

Tables Icon

Table 1 Emission and Absorption Lorentzian Cross-Section Parametersa for Eqs. (6) and (7)

Equations (12)

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A˜(z,ω)=A˜(0,ω)exp{[g(ω)/2+iβ(ω)]z},
A˜(z,ω)=-A(z,T)exp(iωT)dT,
A(z,T)=12π-A˜(z,ω)exp(-iωT)dω.
g(ω)=Γs[σe(ω)N2-σa(ω)N1],
β(ω)=βH(ω)+Γs[σe(ω)N2-σa(ω)N1]/2,
σe,a(λ)=k=1Nre,a Cke,a1+[2(λ-λke,a)/Δλke,a]2,
σe,a(λ)=k=1Nre,a -2Cke,a(λ-λke,a)/Δλke,a1+[2(λ-λke,a)/Δλke,a]2,
β(ω)β0+β1 Δω+β2(Δω)2/2+β3(Δω)3/6,
g(ω)g0+g1 Δω+g2(Δω)2/2,
σOUT=T2-T2,
Tn=inM- nA˜(z,-ω)ωnA˜*(z,-ω)dω.
σOUTσ1=T1T12+β2LT1T12+β3L2T12T12+g1L2β32T13T12+g1L3β2β3T12T1,

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